Complex Systems

Some Parameters Characterizing Cellular Automata Rules Download PDF

Burton Voorhees
Electronic mail address:
Center for Natural and Human Science,
Athabasca University, 1 University Drive,
Athabasca, AB, Canada, T9S 3A3


Three parameters that can be used to characterize aspects of cellular automata behavior are considered for binary valued one-dimensional rules. These are the parameter, the Z parameter, and the obstruction () parameter. After a brief review of the and Z parameters, the parameter is defined and shown to characterize the degree of nonadditivity of a rule. A derivation of the Z parameter in terms of rule table entries is given. It is shown that the parameter and parameter are equal respectively to the area and volume under certain graphs. Finally, the nongenerative 3-site rules are listed in terms of these parameters and their decomposition into additive and nonadditive parts and certain regularities are noted.